Channel tracking using channel covariance estimation

ABSTRACT

Channel tracking is performed using a channel taps covariance matrix. In one embodiment, the channel taps covariance matrix may be used as part of the step term of an adaptive algorithm.

FIELD OF THE INVENTION

[0001] The invention relates generally to communication systems and,more particularly, to techniques and structures for performing channeltracking in such systems.

BACKGROUND OF THE INVENTION

[0002] Many communication devices utilize a channel estimate toaccurately detect data within a signal received from a communicationchannel. In one approach, the channel estimate is used to determine aset of channel taps to be used by an equalizer to remove certain channeleffects from the received signal. In systems where the channelcharacteristics do not change significantly over time (i.e., timeinvariant channels), a single set of channel taps may be determined atthe start of transmission (or before the start of transmission) and usedfor the duration of the subsequent communication. Such a technique isreferred to as preset equalization. In systems where channelcharacteristics are expected to change with time (e.g., in mobilecommunication systems), channel tap adjustments are typically madeperiodically or continuously during the communication in a process knownas adaptive equalization. One form of adaptive equalization that iscommonly implemented in communication systems uses the well knownleast-mean-square (LMS) algorithm to adaptively modify the channel taps.The LMS algorithm is an iterative technique that utilizes a noisyestimate of an error gradient during each iteration to adjust theestimated channel taps in a manner that reduces average mean-squareerror (MSE). As can be appreciated, techniques and structures forenhancing the effectiveness and/or accuracy of LMS-based adaptiveequalization are generally desired.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003]FIG. 1 is a flow chart illustrating a method for processingsignals received from a communication channel in accordance with anembodiment of the present invention; and

[0004]FIG. 2 is a block diagram illustrating receiver functionalitywithin a wireless communication device in accordance with an embodimentof the present invention.

DETAILED DESCRIPTION

[0005] In the following detailed description, reference is made to theaccompanying drawings that show, by way of illustration, specificembodiments in which the invention may be practiced. These embodimentsare described in sufficient detail to enable those skilled in the art topractice the invention. It is to be understood that the variousembodiments of the invention, although different, are not necessarilymutually exclusive. For example, a particular feature, structure, orcharacteristic described herein in connection with one embodiment may beimplemented within other embodiments without departing from the spiritand scope of the invention. In addition, it is to be understood that thelocation or arrangement of individual elements within each disclosedembodiment may be modified without departing from the spirit and scopeof the invention. The following detailed description is, therefore, notto be taken in a limiting sense, and the scope of the present inventionis defined only by the appended claims, appropriately interpreted, alongwith the full range of equivalents to which the claims are entitled. Inthe drawings, like numerals refer to the same or similar functionalitythroughout the several views.

[0006] The present invention relates to techniques and structures forperforming channel tracking within a communication system using achannel tap covariance matrix. In a preferred approach, the covariancematrix is made part of the adaptation algorithm. The channel taps maythen be updated by, among other things, tracking the projection of thechannel on the eigenvectors of the channel covariance matrix. Theinventive principles may be implemented in a wide range of communicationapplications that involve a time varying channel (e.g., systems havingone or more mobile users). The inventive principles may be used, forexample, to enhance the performance of LMS-based based adaptiveequalization schemes. In addition, the principles have application inboth wired and wireless systems.

[0007] In some communication channels, there is no correlation betweenthe changing of one channel tap and the changing of the other channeltaps. In such systems, the channel taps are said to be “statisticallyindependent” of one another. In other channels, the changing channeltaps are correlated to one another. In these systems, the channel tapsare said to be “statistically dependent” upon one another. In conceivingthe present invention, it was appreciated that knowledge about thecorrelation between the changing channel taps in a “statisticallydependent” system could be used to enhance channel tracking performancewithin a communication device. In many wireless communication channels(e.g., those using a pulse shaping filter), the channel taps arestatistically dependent upon one another and significant benefits may bederived by implementing the inventive principles. In the descriptionthat follows, the inventive principles will be discussed in the contextof an LMS-based adaptive equalization scheme. It should be appreciatedthat the inventive principles may also be beneficially implemented insystems using other adaptive equalization techniques.

[0008] In its conventional form, the least-mean-square (LMS) algorithmmay be described by the following equation:

h _(k) =h _(k−1) +μe _(k) s _(k)

[0009] where h _(k) is a column vector of the estimated channel taps atthe time of symbol k, h _(k−1) is the estimated channel taps at the timeof previous symbol k−1, μ is the LMS step factor, e_(k) is thedifference between the expected signal and the actual received signal(i.e., the error), and s _(k) is the complex conjugate of the last Lmodulated symbols at the time of symbol k (where L is the channellength). The error e_(k) may be calculated using the following equation:

e _(k) =s _(k) ^(H) h _(k−1) −y _(k)

[0010] where y_(k) is the received signal sample at the time of symbolk. The LMS step factor μ controls the step size of the tracking. Thisconstant may be optimized based upon the signal-to-noise ratio and theexpected channel changing rate. The values of s _(k) may be derived fromthe output of the equalizer to form a decision-directed adaptiveprocess.

[0011] The covariance matrix of the change in channel may be expressedas a function of the channel taps covariance matrix C as follows:

E[( h _(k) −h _(k−1))( h _(k) −h _(k−1))^(H) ]=bC

[0012] where E[ ] is the expectation function and b is a constant thatdepends upon the changing rate of the channel (which depends uponvehicle speed in wireless communication). For a fading channel, it maygenerally be assumed that each channel tap average changing rate isproportional to its average energy. In one approach, the channel tapcovariance matrix C is estimated as follows:$\underset{\underset{\_}{\_}}{\hat{C}} = {{E\left( {\underset{\_}{h\quad h}}^{H} \right)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{\underset{\_}{h}}_{i}{\underset{\_}{h}}_{i}^{H}}}}}$

[0013] where N is the number of training sequences used for estimatingthe covariance matrix and h _(i) is the vector of channel taps attraining sequence i. The covariance matrix may also be estimated basedon knowledge about the filters in the transmitter and receiver. Othermethods for estimating or calculating the channel taps covariance matrixC are also known. The covariance matrix C may be described as acombination of its eigenvectors and eigenvalues as follows:

C=VΛV ^(H)

[0014] where Λ is the diagonal matrix of eigenvalues of C and V is amatrix whose columns are the corresponding eigenvectors of C. Thechannel tap vector h may be decomposed into the eigenvectors V asfollows:

h _(k)=V D _(k)

[0015] where D _(k) are the coefficients of each eigenvector (D_(k)˜N(0,Λ)). The projection of the conventional LMS step on the channeleigenvectors is expressed as:

V ^(H)μe_(k) s _(k)

[0016] Using this projection, the coefficients D _(k) are updatedaccording to the following equation:

D _(k) =D _(k−1) +Uμe _(k) V ^(H) s _(k)

[0017] where U is the diagonal matrix of the square root of theeigenvalues (VUV ^(H)=C ^(½)). Multiplying the above equation by thematrix V gives:

V D _(k) =V D _(k−1) +μe _(k) VUV ^(H) s _(k); or

h _(k) =h _(k−1) +μe _(k) VUV ^(H) s _(k)

[0018] This last equation may be rewritten as:

h _(k) =h _(k−1) +μe _(k) C ^(½) s _(k)

[0019] where C ^(½) is the square root of the covariance matrix C. Thisis a modified version of the conventional LMS algorithm.

[0020] If the taps associated with a communication channel arestatistically independent of one another, the covariance matrix will bea unit matrix (or a unit matrix multiplied by a constant) and the abovemodified LMS algorithm will reduce to the conventional LMS algorithmdescribed previously. If the taps associated with a communicationchannel are statistically dependent upon one another, on the other hand,the covariance matrix will not be diagonal and the modified algorithmset out above may be used to significantly enhance the error rateperformance of a system over the conventional algorithm. As describedabove, most wireless communication systems being deployed today havechannel taps that are statistically dependent.

[0021]FIG. 1 is a flow chart illustrating a method for processingsignals received from a wireless communication channel in accordancewith an embodiment of the present invention. In one approach, the methodis implemented within a modulation-demodulation device (i.e., a modem),although other implementations are also possible. First, an initialchannel estimation is performed using a received signal and a prioriknowledge (e.g., training sequences) of the corresponding transmitteddata (block 10). In one approach, the least squares (LS) method is usedto perform the initial channel estimation, although other methods mayalternatively be used. The initial channel estimation may generate avector of channel tap values for each of a plurality of trainingsequences used. A channel tap covariance matrix C is estimated based onthe estimated channel (block 12). In one approach, this matrix isestimated using the following equation:$\underset{\underset{\_}{\_}}{\hat{C}} = {{E\left( {\underset{\_}{h\quad h}}^{H} \right)} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{\underset{\_}{h}}_{i}{\underset{\_}{h}}_{i}^{H}}}}}$

[0022] where N is the number of training sequences used for estimatingthe covariance matrix and h _(i) is the vector of channel taps attraining sequence i. The covariance matrix C is then multiplied by aconstant b related to the channel changing rate to generate a tapschanging covariance matrix (block 14). The constant b is normallyapplication specific and will typically, be optimized depending on thechannel fading process. A square root of the taps changing covariancematrix is next determined (block 16). As described previously, thissquare root information is used within the modified LMS algorithm.Eigenvalue LMS tracking is then performed to update the estimatedchannel taps based on newly received data and decision information fedback from an equalizer (block 18). As described previously, in oneapproach, the updates are made according to the modified LMS algorithm:

h _(k) =h _(k−1) +μe _(k) C ^(½) s _(k)

[0023] The updated channel taps are transferred to the equalizer whichuses them to process corresponding signals received from the channel todetect data therein (block 20). In some cases, it is expected that thecovariance matrix C will change slowly so that the eigenvectors may onlyneed to be determined (e.g., by calculating the square root of thecovariance matrix) at intervals (e.g., once every X slots) rather thancontinuously. Alternatively, an algorithm may be used to track theprojection of the channel on the eigenvectors. In some cases, it may besufficient to track only the projection of the channel on theeigenvector(s) with the highest eigenvalue(s). The projection of thechannel on other vectors may be left unchanged (not tracked). One methodof doing this is by replacing small eigenvalues in the matrix ofeigenvalues by zero. The covariance matrix C will normally be banddiagonal.

[0024]FIG. 2 is a block diagram illustrating receiver functionalitywithin a wireless communication device 30 in accordance with anembodiment of the present invention. The communication device 30 mayinclude any of a wide variety of different devices including, forexample, mobile devices (e.g., a cellular telephone or other handheldcommunicator, a laptop computer or personal digital assistant (PDA)including wireless transceiver functionality, etc.) and stationarydevices (e.g., a basestation transceiver, etc.). As illustrated, thecommunication device 30 includes: an antenna 32, a receiver front end34, a channel estimator 36, a channel tracking unit 38, an equalizer 40,a deinterleaver 42, a channel decoder 44, a source decoder 46, and aninformation sink 48. The antenna 32 is operative for receiving signalsfrom a wireless communication channel. The antenna 32 may also act as atransmit antenna for the device 30. The receiver front end 34 convertssignals received from the wireless channel into a basebandrepresentation that is more easily processed within the device.

[0025] When a communication link is first being established, a pluralityof training sequences are transmitted to the communication device 30through the wireless communication channel. The training sequences arereceived by the antenna 32 and converted to a baseband representation bythe receiver front end 34. The received training sequences are theninput into the channel estimator 36 which uses the received sequences todetermine initial channel estimates for the wireless channel (using, forexample, a least squares approach). The channel estimator 36 may have apriori knowledge of the transmitted training sequences which it comparesto the received signals to determine the initial channel estimates. Theinitial channel estimates may then be delivered to the channel trackingunit 38. Eventually, the transmission of training sequences to thecommunication device 30 ends and the transmission of user data begins.The data signals are received by the antenna 32 and converted to abaseband representation within the receiver front end 34. The datasignals are then delivered to the input of the equalizer 40 whichfilters the signals in a manner dictated by the channel taps currentlybeing applied to the equalizer 40. The equalizer 40 may include any typeof equalizer structure (including, for example, a transversal filter, amaximum likelihood sequence estimator (MLSE), and others). When properlyconfigured, the equalizer 40 may reduce or eliminate undesirable channeleffects within the received signals (e.g., inter-symbol interference).

[0026] The received data signals are also delivered to the input of thechannel tracking unit 38 which uses the received signals to track thechannel taps applied to the equalizer 40. During system operation, thesetaps are regularly updated by the channel tracking unit 38 based onchanges in the wireless channel. In addition to the receive data, thechannel tracking unit 38 also receives data from an output of theequalizer 40 as feedback for use in the channel tracking process. Thechannel tracking unit 38 uses the initial channel estimates determinedby the channel estimator 36 to determine the channel taps covariancematrix (C). The channel tracking unit 38 then determines the value ofthe constant b (related to the channel changing rate) and calculates thetaps changing covariance matrix (b*C). The square root of the tapschanging covariance matrix is then determined and used within themodified LMS algorithm to determine the updated channel taps, which arethen applied to the equalizer 40. The output of the equalizer 40 isdeinterleaved in the deinterleaver 42. Channel and source coding is thenremoved from the signal in the channel decoder 44 and the source decoder46, respectively. The resulting information is then delivered to theinformation sink 48 which may include a user device, a memory, or otherdata destination.

[0027] Although the present invention has been described in conjunctionwith certain embodiments, it is to be understood that modifications andvariations may be resorted to without departing from the spirit andscope of the invention as those skilled in the art readily understand.Such modifications and variations are considered to be within thepurview and scope of the invention and the appended claims.

What is claimed is:
 1. A communication apparatus comprising: means forobtaining channel taps associated with a communication channel; meansfor determining a channel taps covariance matrix for said communicationchannel using said channel taps; and means for updating said channeltaps using said channel taps covariance matrix.
 2. The communicationapparatus of claim 1, wherein: said means for determining a channel tapscovariance matrix includes means for estimating said channel tapscovariance matrix based upon the following equation:$\underset{\underset{\_}{\_}}{\hat{C}} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{\underset{\_}{h}}_{i}{\underset{\_}{h}}_{i}^{H}}}}$

where N is the number of training sequences used for estimating thechannel taps covariance matrix and h _(i) is a vector of channel taps attraining sequence i.
 3. The communication apparatus of claim 1, wherein:said means for updating said channel taps includes means for multiplyingsaid channel taps covariance matrix by a constant related to a changingrate of said channel to achieve a taps changing covariance matrix. 4.The communication apparatus of claim 3, wherein: said means for updatingsaid channel taps includes means for determining a square root of saidtaps changing covariance matrix.
 5. The communication apparatus of claim1, wherein: said means for updating said channel taps includes means forimplementing the following equation: h _(k) =h _(k−1) +μe _(k) C ^(½) s_(k) where h _(k) represents the channel taps at the time of a symbol k,h _(k−1) represents the channel taps at the time of a previous symbolk−1, μ is a step factor, e_(k) is an error between an expected signaland an actual received signal, s _(k) is a complex conjugate of a numberof previous symbol decisions at the time of symbol k, and C ^(½) is thesquare root of the covariance matrix C.
 6. A communication apparatuscomprising: an equalizer to process signals received from acommunication channel to reduce channel effects within said signals,said equalizer including at least one input to receive channel taps foruse in configuring said equalizer; and a channel tracking unit to updatesaid channel taps based upon an output of said equalizer and acovariance matrix associated with said channel taps.
 7. Thecommunication apparatus of claim 6, wherein: said channel tracking unitincludes a covariance matrix estimator for estimating said covariancematrix associated with said channel taps.
 8. The communication apparatusof claim 7, wherein: said channel tracking unit includes amultiplication unit for multiplying said estimated covariance matrix bya constant related to a changing rate of said communication channel togenerate a taps changing covariance matrix.
 9. The communicationapparatus of claim 8, wherein: said channel tracking unit includes asquare root unit to determine a square root of said taps changingcovariance matrix.
 10. The communication apparatus of claim 6, wherein:said channel tracking unit updates said channel taps using the followingequation: h _(k) =h _(k−1) +μe _(k) C ^(½) s _(k) where h _(k)represents the channel taps at the time of a symbol k, h _(k−1)represents the channel taps at the time of a previous symbol k−1, μ is astep factor, e_(k) is an error between an expected signal and an actualreceived signal, s _(k) is a complex conjugate of a number of previoussymbol decisions at the time of symbol k, and C ^(½) is the square rootof the covariance matrix C.
 11. The communication apparatus of claim 6,wherein: said channel tracking unit includes means for tracking aprojection of the channel on eigenvectors associated with saidcovariance matrix.
 12. The communication apparatus of claim 11, wherein:said means for tracking only tracks the projection of the channel oneigenvectors having associated eigenvalues that exceed a predeterminedvalue.
 13. A method for performing channel tracking in a communicationsystem comprising: obtaining channel taps associated with acommunication channel; estimating a channel taps covariance matrix forsaid communication channel using said channel taps; and updating saidchannel taps based on said channel taps covariance matrix.
 14. Themethod of claim 13, wherein: estimating a channel taps covariance matrixfor said communication channel includes calculating the followingsummation:$\underset{\underset{\_}{\_}}{\hat{C}} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{\underset{\_}{h}}_{i}{\underset{\_}{h}}_{i}^{H}}}}$

where N is the number of training sequences used for estimating thecovariance matrix and h _(i) is the vector of channel taps at trainingsequence i.
 15. The method of claim 13, wherein: updating includes usinga modified least mean square (LMS) algorithm to calculate new values forsaid channel taps, said modified LMS algorithm using said channel tapscovariance matrix.
 16. The method of claim 15, wherein: said modifiedLMS algorithm is expressed as follows: h _(k) =h _(k−1) +μe _(k) C ^(½)s _(k) where h _(k) represents the channel taps at the time of a symbolk, h _(k−1) represents the channel taps at the time of a previous symbolk−1, μ is a step factor, e_(k) is an error between an expected signaland an actual received signal, s _(k) is a complex conjugate of a numberof previous symbol decisions at the time of symbol k, and C ^(½) is thesquare root of the covariance matrix C.
 17. A computer readable mediumhaving program instructions stored thereon for implementing, whenexecuted within a digital processing device, a method for performingchannel tracking, said method comprising: obtaining channel tapsassociated with a communication channel; estimating a channel tapscovariance matrix for said communication channel using said channeltaps; and updating said channel taps based on said channel tapscovariance matrix.
 18. The computer readable medium of claim 17,wherein: estimating a channel taps covariance matrix for saidcommunication channel includes calculating the following summation:$\underset{\underset{\_}{\_}}{\hat{C}} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{{\underset{\_}{h}}_{i}{\underset{\_}{h}}_{i}^{H}}}}$

where N is the number of training sequences used for estimating thecovariance matrix and h _(i) is the vector of channel taps at trainingsequence i.
 19. The computer readable medium of claim 17, wherein:updating includes using a modified least mean square (LMS) algorithm tocalculate new values for said channel taps, said modified LMS algorithmusing said channel taps covariance matrix.
 20. A communication apparatuscomprising: an equalizer to process signals received from acommunication channel, said equalizer having a transfer function thatdepends upon a plurality of channel taps; a channel estimator todetermine initial channel taps for said communication channel; and achannel tracking unit to track said plurality of channel taps over time,said channel tracking unit including: a covariance matrix estimator toestimate a covariance matrix associated with said plurality of channeltaps; and an update unit to update said plurality of channel taps basedon said estimated covariance matrix.
 21. The communication apparatus ofclaim 20 wherein: said channel estimator determines said initial channeltaps using training sequences received from said wireless communicationchannel, said channel estimator having a priori knowledge of saidtraining sequences.
 22. The communication apparatus of claim 20 wherein:said channel estimator determines said initial channel taps using aleast squares technique.
 23. The communication apparatus of claim 20wherein: said covariance matrix estimator estimates an initialcovariance matrix based on an output of said channel estimator.
 24. Thecommunication apparatus of claim 20 wherein: said update unit updatessaid plurality of channel taps based on the following equation: h _(k)=h _(k−1) +μe _(k) C ^(½) s _(k) where h _(k) represents the channeltaps at the time of a symbol k, h _(k−1) represents the channel taps atthe time of a previous symbol k−1, μ is a step factor, e_(k) is an errorbetween an expected signal and an actual received signal, s _(k) is acomplex conjugate of a number of previous symbol decisions at the timeof symbol k, and C ^(½) is the square root of the covariance matrix C.